The solution of the differential equation x dy - dx - y -3 represents a family ofA- straight linesB- circlesC- parabolasD- ellipses

The correct option is A straight lines nbsp; nbsp;xdy/dx y=3 ⇒dy/y+3=dx/x Integrating both sides, we get nbsp; log|y+3|=log|x|+log |C| ⇒ nbsp; |y+3|=|C ...

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Standard XII

Mathematics

Differential Equations Definition

The solution ...

Question

The solution of the differential equation $x \frac{d y}{d x} - y = 3$ represents a family of

straight lines

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circles

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parabolas

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ellipses

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Solution

The correct option is A straight lines
$x \frac{d y}{d x} - y = 3$
$\Rightarrow \frac{d y}{y + 3} = \frac{d x}{x}$
Integrating both sides, we get
$log | y + 3 | = log | x | + log | C |$
$\Rightarrow | y + 3 | = | C x |$ which represents a family of straight lines.

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The solution of the differential equation xdydx−y=3 represents a family of

The correct option is A straight lines xdydx−y=3 ⇒dyy+3=dxx Integrating both sides, we get log|y+3|=log|x|+log|C| ⇒|y+3|=|Cx| which represents a family of straight lines.

The solution of the differential equation $x \frac{d y}{d x} - y = 3$ represents a family of

The correct option is A straight lines
$x \frac{d y}{d x} - y = 3$
$\Rightarrow \frac{d y}{y + 3} = \frac{d x}{x}$
Integrating both sides, we get
$log | y + 3 | = log | x | + log | C |$
$\Rightarrow | y + 3 | = | C x |$ which represents a family of straight lines.